更快的傅里叶变换？$\mathcal{O}(N^2)$时间宇宙学模拟中小尺度功率谱和双谱的计算
A Faster Fourier Transform? Computing Small-Scale Power Spectra and Bispectra for Cosmological Simulations in $\mathcal{O}(N^2)$ Time
摘要：
我们提出了宇宙学模拟中小尺度功率谱和双谱的$\mathcal{O}(N^2)$估计。与传统方法相结合，这些方法允许在大范围的尺度上有效地计算光谱，比单独基于快速傅立叶变换的方法需要少几个数量级的计算时间。这些方法适用于任何示踪剂，模拟粒子，晕或星系，并利用简单的几何形状的盒子和周期性，以消除几乎所有的依赖于大型随机粒子目录。通过在配置空间中工作，功率谱和双谱都可以通过直到某个半径的粒子对的加权和来计算，这可以在较大的$k$下减少，从而导致在小尺度上具有降低的复杂度的算法。这些不受混叠或散粒噪声的影响，允许将光谱计算为任意大的波数。估计严格推导和测试模拟，并讨论其协方差。附带的代码HIPSTER已经公开发布，其中包含了这些算法。这样的估计量将是很大的使用在大型高分辨率模拟集的分析。
英文摘要：
We present $\mathcal{O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales, requiring orders of magnitude less computation time than Fast Fourier Transform based approaches alone. These methods are applicable to any tracer; simulation particles, halos or galaxies, and take advantage of the simple geometry of the box and periodicity to remove almost all dependence on large random particle catalogs. By working in configuration-space, both power spectra and bispectra can be computed via a weighted sum of particle pairs up to some radius, which can be reduced at larger $k$, leading to algorithms with decreasing complexity on small scales. These do not suffer from aliasing or shot-noise, allowing spectra to be computed to arbitrarily large wavenumbers. The estimators are rigorously derived and tested against simulations, and their covariances discussed. The accompanying code, HIPSTER, has been publicly released, incorporating these algorithms. Such estimators will be of great use in the analysis of large sets of high-resolution simulations.
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